{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:STLGDWEBW6V3B6MIMPN77H3UCY","short_pith_number":"pith:STLGDWEB","schema_version":"1.0","canonical_sha256":"94d661d881b7abb0f98863dbff9f741639a15f8b303626b0788d2f05fd95f038","source":{"kind":"arxiv","id":"1402.0441","version":1},"attestation_state":"computed","paper":{"title":"Representations of ideals in Polish groups and in Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Barnabas Farkas, Grzegorz Plebanek, Piotr Borodulin-Nadzieja","submitted_at":"2014-02-03T17:34:31Z","abstract_excerpt":"We investigate ideals of the form $\\{A \\subseteq \\omega\\colon \\sum_{n\\in A} x_n$ is unconditionally convergent $\\}$, where $(x_n)_{n\\in\\omega}$ is a sequence in a Polish group or in a Banach space. If an ideal on $\\omega$ can be seen in this form for some sequence in $X$, then we say that it is representable in $X$.\n  After numerous examples we show the following theorems: (1) An ideal is representable in a Polish Abelian group iff it is an analytic P-ideal. (2) An ideal is representable in a Banach space iff it is a non-pathological analytic P-ideal.\n  We focus on the family of ideals represe"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1402.0441","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-02-03T17:34:31Z","cross_cats_sorted":[],"title_canon_sha256":"8a774697381dfdc19efab48b08a50d67f02e2fddf6a6b0ebfe01f6e39848d2a7","abstract_canon_sha256":"eaac178029bc54ee0d6dbfe7b4e14e4e6c9762799693ab397159a0d975d680b2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:00:15.288659Z","signature_b64":"R33vvdc5n6w8h0imzBtQdowRII+sAsXN0IAjSpGnqcmOdYDm3j03HGcLZwGfGmGge9IG6dv/mVH1wCHe3HkwDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"94d661d881b7abb0f98863dbff9f741639a15f8b303626b0788d2f05fd95f038","last_reissued_at":"2026-05-18T03:00:15.287877Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:00:15.287877Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Representations of ideals in Polish groups and in Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Barnabas Farkas, Grzegorz Plebanek, Piotr Borodulin-Nadzieja","submitted_at":"2014-02-03T17:34:31Z","abstract_excerpt":"We investigate ideals of the form $\\{A \\subseteq \\omega\\colon \\sum_{n\\in A} x_n$ is unconditionally convergent $\\}$, where $(x_n)_{n\\in\\omega}$ is a sequence in a Polish group or in a Banach space. If an ideal on $\\omega$ can be seen in this form for some sequence in $X$, then we say that it is representable in $X$.\n  After numerous examples we show the following theorems: (1) An ideal is representable in a Polish Abelian group iff it is an analytic P-ideal. (2) An ideal is representable in a Banach space iff it is a non-pathological analytic P-ideal.\n  We focus on the family of ideals represe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0441","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1402.0441","created_at":"2026-05-18T03:00:15.288002+00:00"},{"alias_kind":"arxiv_version","alias_value":"1402.0441v1","created_at":"2026-05-18T03:00:15.288002+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.0441","created_at":"2026-05-18T03:00:15.288002+00:00"},{"alias_kind":"pith_short_12","alias_value":"STLGDWEBW6V3","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_16","alias_value":"STLGDWEBW6V3B6MI","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_8","alias_value":"STLGDWEB","created_at":"2026-05-18T12:28:49.207871+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/STLGDWEBW6V3B6MIMPN77H3UCY","json":"https://pith.science/pith/STLGDWEBW6V3B6MIMPN77H3UCY.json","graph_json":"https://pith.science/api/pith-number/STLGDWEBW6V3B6MIMPN77H3UCY/graph.json","events_json":"https://pith.science/api/pith-number/STLGDWEBW6V3B6MIMPN77H3UCY/events.json","paper":"https://pith.science/paper/STLGDWEB"},"agent_actions":{"view_html":"https://pith.science/pith/STLGDWEBW6V3B6MIMPN77H3UCY","download_json":"https://pith.science/pith/STLGDWEBW6V3B6MIMPN77H3UCY.json","view_paper":"https://pith.science/paper/STLGDWEB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1402.0441&json=true","fetch_graph":"https://pith.science/api/pith-number/STLGDWEBW6V3B6MIMPN77H3UCY/graph.json","fetch_events":"https://pith.science/api/pith-number/STLGDWEBW6V3B6MIMPN77H3UCY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/STLGDWEBW6V3B6MIMPN77H3UCY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/STLGDWEBW6V3B6MIMPN77H3UCY/action/storage_attestation","attest_author":"https://pith.science/pith/STLGDWEBW6V3B6MIMPN77H3UCY/action/author_attestation","sign_citation":"https://pith.science/pith/STLGDWEBW6V3B6MIMPN77H3UCY/action/citation_signature","submit_replication":"https://pith.science/pith/STLGDWEBW6V3B6MIMPN77H3UCY/action/replication_record"}},"created_at":"2026-05-18T03:00:15.288002+00:00","updated_at":"2026-05-18T03:00:15.288002+00:00"}